Studies: Volume to ship mass ratios

[Vandermeer (OP)]

In the past I have made several approaches towards trying to figure out how big Aurora ships actually are. Either I converted the ship mass coming from Aurora, or I took some given diameters from other sources, and tried to come up with mass. Nearly all these calculations were pretty ad-hoc though, except maybe for one time where I tried to find the actual thickness of armor (in cm) for certain ship sizes, as it mattered for calculating the radiation penetration.

However, I never sat down and really dealt with this core issue that was floating over the horizon, and that is to figure out a good estimate of a volume to mass ratio, so when you know either of the two, you can also pretty much know the other to some degree of accuracy. This matters a lot for me to know, but is obviously just a role playing issue where you would need it to fill your imagination, or maybe also sometimes if one wants to import ships from franchises that only give one or the other number.

So since Aurora is basically 100% inspired by naval warfare and their ships, I figured that I could just compare their volume and mass data, and did some research. The estimations I did in the past on this were always just based of a single design mostly (Nimitz aircraft carrier for example), rather than a greater comparison chart. This time I also tried to be as accurate as possible, as getting the volume can be quite a mystery for anything that is shaped rather organically such as ships.
The following chart has thus a good degree of error left that comes from that I had to basically guess how much space a certain design would fill if reduced to cuboid object. This was done by cutting down the width and height of any ship I had in a way so that you could imagine the "overflow" beyond that line to fit in exactly with the gaps that still were inside those new borders. Quick concept illustration (wouldn't agree on accuracy here):





There are two substantial weaknesses resulting from this method.

1. Most notable is that the volume may vary quite a bit due to that I never had any data on the real height of any of the ships. This is because sea ships get measured only by their draught, so I only had the water line to work with. Since the ratio between this water line and the rest of the design was nearly never obvious, I had to pretty much guess the remaining height. To make the error source uniform at least, I went with exact factor 2 for the 'effective cuboid height', as this seems to match many ships, just like you can also see in the picture above. (..which I just randomly drew from the internet btw.)
I would like to think that any exception to this rule gets evened out by the amount of entries that I did, so the error vanishes in the mass to a good level. For any singular ship entry I would expect as much as +/- 25% volume error from this source alone though.

2. Figuring out volume to mass ratios in this way is ignorant of the difference that result from better conservation of volume the greater the ship is. For example, if you coat a 5km³ and a 40km³ ship with 30mm armor, the 40km³ won't weight 8 times as the 5km³ one anymore, because it doesn't have as much surface that needs to be covered with such armor in comparison to its total volume. So in short, you can expect larger ships to get higher V/M (volume to mass ratios), as mass should not grow as fast as the space it occupies.
I however found that this error is marginal for the naval ships at least, first because they do not differ in size too extremely, and second, well, the data actually shows the opposite: Small ships as corvettes seem pretty light for their dimensions, while battleships and carriers appear to be especially heavy. I could think that this is due to the fact that they increase armor disproportionally to make the larger and more expensive ships extra save and "not as expendable" as smaller ones, but I am really not sure what makes them so heavy. Maybe there is some hidden factor that causes this, and if you know it or have some idea, I would certainly like to hear this.

So here come the charts:




Everything has a sub total to see the difference in design groups, but the grand total for the mass to volume factor is 4.57m³ per t of weight.

The ton by man ratio was not actually my objective here, and I just included it, well, because I looked at data anyway. It seemed unfair to me to throw it together, as it really is a part of design mission. However, I saw that most of the ships actually fell in a pretty unison line with this (only 2-3 extremes that didn't match), so I figured a total average could be made too as some sort of reference. It came out as 24.78 tons per man here; quite a bit more than you usually have in Aurora. (I always called Aurora ships overpopulated, and here is the evidence . ~ This is not even counting the hypothetical extra equipment that water and oxygen refinement would need on an actual spaceship, as well as some extra redundancy in the support barren empty space)
Nothing against the amazing 5000 tons per man that you get in all Federation ships, or still somewhat high 290 tons per man that I found when taking apart the Warhammer 40k dictator cruiser.(and those are described as having extremely uncushy pressed military quarters which actually reduce morale --- I guess engines for star ships may add way more mass than they take on any conventional ship,... or the writers did not think this through as much )

[Vandermeer (OP)]

Screw that last part about the ton per man ratio though. I just followed an intuition, and yes, the ton by man ratios in Aurora actually just refer to the crew quarter space they need, not total size of course. Actual ton per man ratio is more towards 35-45, so that pretty much nails it I guess when considering the part about the needed extra equipment. Shame on me for never noticing this simple fact earlier.(no one ever called me out for it though too. )

[TT]

Maybe for your purposes it doesn't matter, but I feel compelled to point out that tonnage in naval warfare doesn't directly measure the mass of the vessel.  I believe tonnage refers to the amount of water the ship displaces when it floats.  I don't know if that is what Aurora's tonnage represents (and since the ships in Aurora don't float, I suspect that tonnage represents something different), but I don't think the tonnage represents ship mass.

[Vandermeer (OP)]

Oh, water displacement does actually directly represent the ship's mass. The water that gets displaced is of course directly proportional to the real mass that the ship has.(why would it be any different?) In some way you could say that the sea water is nothing but a large scale on which you drop the ship. Each cubic meter of water that has to yield is now exactly equal to one ton weight of the ship.(now, if you talk about different densities of water, there will be a slight offset maybe, but I think that is a slim percentile error, and I doubt the officially stated values didn't take that into account too)

I know why you confused this though, because when an object is completely submerged into water (such as sinking objects with higher density than water), it of course only displaces an amount equal to its own volume, so there is no way of knowing the mass just from this. However, ships have a lesser density than water, causing them to be a floating object of course, and those only sink in to a percentile that is their density compared to the water density. A direct weight scale.

[TT]

I stand corrected.  After reading your response I looked into this and you are correct.  Naval tonnage represents the water displaced, which is the actual weight of the ship.  Thank you for making me a little smarter tonight.

[MarcAFK]

Naval vessels haven't been heavily armoured since the end of world war two, I think at the moment you see some quantity of soft flack/shrapnel armour around the bridge and important areas like fire control for weapons, and ammunition storage is heavily armoured between itself to prevent ammunition explosion taking down a whole ship, but for the most part armour isn't a significant part of a modern ships weight. This affects any comparison between modern navy's and Aurora since armour is effective in aurora, and for the most part is a significant fraction. 
Also a quick calculation using your density ratio shows a 50 ton object to be roughly a 6 meter cube.

[Vandermeer (OP)]

I stand corrected.  After reading your response I looked into this and you are correct.  Naval tonnage represents the water displaced, which is the actual weight of the ship.  Thank you for making me a little smarter tonight.

Glad to be of service.


@Marc: If it isn't armor, then I really wonder what else it could be. Maybe a larger fuel storage, or the ratio of needed corridors becomes more efficient? It really sticks out that this appears so broadly over all larger ships with no real exception.
Good point that with the armor offsetting quite a bit in Aurora. I think I will try to figure out a correction factor for this later on. Hmm, for this I need to find the data of armor for those ships, and then to this mass-cover calculation in Aurora again. Luckily Aurora directly referenced total armor weight. If the difference is too high, then I think I can derive a correction for each ship.

The 50t=6³m³, yes, that is real. Looks good I think. Oh, did we just figure out what 1HS is? :O
Only problem I see is with fighters, where it might need a separate comparison.(one quick calculation showed a ratio there to be more in the 10-11 area) However, that is for our worldly fighters of 20-40 tons, and not those 500t Aurora behemoths. There were quite small corvettes in this chart, who went down to 650t and were still in line with the rest of the data pretty much, so the corvette sub-ratio might just work out here as well.

[MarcAFK]

Another interesting thing I just discovered, during the cold war it became standard for most of an American warships's structure to be aluminium, lighter equals faster which is a more useful defence against missiles, also it makes them cheaper to build and run, however after the 1975 collision of the USS Belknap with the carrier John F. Kennedy the subsequent structural damage caused future designs to use more steel. Also the structural aluminium itself burning during the extreme heat of the fire might have been a contributing factor.

Actually looking at your chart it strikes me that the more modern ships have a much higher volume to mass, while the most heavily armoured Bismark and Yamamoto are the densest. Except for carriers which are an anomaly, I would be cautious however as your estimation method probably fails on carriers due to the extreme overhang of the flight deck combined with the unusual dimensions. Even though flight decks are usually well armoured it may not be significant because : "Since USS Theodore Roosevelt, the carriers have been constructed with 2.5 in (64 mm) Kevlar armor over vital spaces, and earlier ships have been retrofitted with it".  Kevlar cloth alone weighs something like 14g per sqm for .2 mm. so that's 4.5 kg ler square meter, if the flight deck was armoured this way (I'm not suggesting it is) that alone would be only 82 tons for 4.5 acres of deck. Overall I think even if the whole ship was armoured this way it would be a drop in the bucket for a 100,000 ton ship.
Edited because I contradicted myself somewhat.

[Vandermeer (OP)]

If figure this mass growth has to do with larger fuel reserves. Large ships are often considered as a supplier for fleets, so you would have to have extra stashes to not draw from original range. Is just hypothesis though.

With the carriers and flight deck: I did consider this already. What I did was to take 1/3rd of the difference between waterline and flight deck here as some sort of corrected width, and then reduce this new number as a factor. For a quick example, with the Nimitz I took (76m flight deck - 41m waterline)/3 + waterline = ~53m corrected width.
So this is already in the numbers for the carriers above, but it is admittedly quite random of a correction, and even more so after feeling rather than real measurement. Still better than just taking the oversized flight deck for a scale, which would have meant all those carrier numbers needed to be much smaller. Now it is only extra +/-20% error that can ease out in the average a little.

[Vandermeer (OP)]

So I have been coming back to this, and am now considering the armor thing. For this to work I have to figure out how much armor weights in Aurora for certain sizes, and then pretty much exclude that, or come up with table of corrections depending on tech level.
The "problem" here is that Aurora is commendably realistic in how it calculates the armor coverage, as it includes the law of mass conservation becoming more effective on bigger objects, which leads to increasingly lighter armor despite same protection(/thickness).

In case it is unclear what this is about, here is an illustration which should explain it:


I never knew if this really worked this way for sure so far in Aurora. I only realized that armor seemed to become lighter and lighter percentage wise the larger the ship grew, so this reminded me of this law of course. Before applying any correction to the bigger ship list above, this had to be proven, so I made some tests and this table:



To explain a bit - I first made a ship of basic components until it reached the round number mark you see in the first column (1k,2k, etc.), and then recorded the armor that built on top of it.(which is conventional armor btw.) The mass you see in the other 5 columns thus is added to that as the 'mass of the armor' covering the hull. For example a 7k hull with 3 armor layers actually weights 10130t.
Then, the first column was obviously tricky to get here for the area information, as there is no 0 armor, but it was possible by simply creating designs of that size which already included 1 armor instead.(for example a 1k maybe included 220t armor already) It turned out that this lead to the exact same numbers, already hinting that there was a noble streamlined sizing rule governing Aurora's calculations.

It worked out well, as it indeed proves that Aurora uses the law above. For a quick direct example you can see that the 24k sized ship, which is exactly of 2 times the dimensions (=x8 mass) as the 3k sized one, has exactly 4 times the area, and thus exactly 4 times the armor weight.(which you cannot see in the first column though) Another close coming example is 1 layer 7k (7885 t) against 1 layer 60k (63545 t), which also nearly has this x8 mass difference, and the armor clearly also nearly weights 4 times as much.
Of course I made exact calculations to test this through. For that you have to use this formula:





Except of around +-0.2 errors from the rounding Aurora does, it is indeed accurate in all cases. So that worked.?

Next step is generating an excel column to the chart of the first post to see how much mass-% of any of those ships would in Aurora actually be armor (on standard 1 layer designs of course). Steel density then leads to a correction factor for every design, and hopefully a rule appears, so life is easier. Didn't get to it today though.
..And I still have no idea what causes the bigger ships from the chart in the first post be so much heavier. Marc said there is near to no armor on recent ships anymore, so maybe this effect does simply not appear, and the tendency to include more fuel on larger ships is what increases the density slowly. ..But again, still no proof.

[MarcAFK]

I'm thinking that it's probably due to automation leading to denser more efficient use of space, as well as a conscious design effort to reduce cross section which improves top speed and fuel efficiency.
I love the effort that went to the chart and the diagram is excellent for getting such a simple concept across for a casual like myself.
Edit: wait, I had that backwards, modern ships are less dense so I'll completely ignore how wrong I was and instead suggest modern ships are built significantly more cheaply, lighter grade metal across the board, more plastics and composites etc. Even ignoring the actuall hull most individual components that goes into a ship would be significantly lighter now than it was back in the 40's.
For comparison.
As a counter example I present the 5 inch mark 45 naval gun which is a standard part of American destroyers and cruisers.
The 80's era mark 2 weighed in at 21,691 kg while the slightly more capable year 2000 model mark 4 is a hefty 28,924 kg .
Computers and environmental systems are presumably lighter now, but theres probably a lot of variables I'm not qualified to estimate about.
Since WW2 guns have used smokeless powder which has significantly different properties than gunpowder, assuming a new shell must produce similar pressure than an older one in order to be used in the same gun barrel than using powder with 2-3 times the energy density might allow a lighter propellant weight, this might be offset by adding something that causes a slower burn rate which would lower the extreme initial pressure but allow greater muzzle velocity. So shells and missiles 'might' be lighter, but once again I can't really find much supporting data, best would be to find the weight of actual ship systems.
This chart of powder densities is pretty handy for my heavily modded Kerbal Space Program though.

Also I realise that specific impulse is not 100% energy density, but it's generally a pretty close approximation.

[Paul M]

Just keep in mind that a naval ship must float.  This means it must have a final density that is less than water.  A spacecraft does not need to float, but (obviously not in aurora) needs to consider that the acceleration it can achieve (which determines its velocity) is limited by being the Force applied divided by the mass of the ship...where mass is volume*density.

Also modern ships are again built with armour in mind...the previous mistake was corrected after the falklands war when the discovered that a missile hit does not spell the doom of the ship but having the ship catch fire due to the aluminum structure igniting does.  Modern ships are also slower than WW2 ships stupidly enough, but I suspect that is more because you compare a modern DD to a WW2 DD and you should more reasonably compare it to a WW2 CA or CL.  Also naval speeds has far less to do with the mass of the ship anyway and more to do with the limits imposed by fluid dynamics.

As a first guess Aurora ships size is determined primarily by the volume needed for the crew space.  Work stations, maintenance spaces, walk ways, mess halls, kitchens, medical facilities, sleeping areas and toilets probably define the volume of most of the ship.  Missile magazines, cargo, fuel, hangers spaces probably are the other major volume components.  These are also the "low density" components of the ship being largely air.  After that you have the various plants and things like beam weapons which are mass intensive but volumetrically small.

Also a cargo ship might be just a spar with a small-ish crew volume and mostly just empty space one attached containers to.

To determine an average size of an aurora ship you first need to know the approximate density of any particular component and that defines the volume it occupies if you accept the mass as a given.  Or you need to know its approixmate volume (if you figure that is correct) and then knowing the density you find the ships final mass. 

[Vandermeer (OP)]

Also modern ships are again built with armour in mind...the previous mistake was corrected after the falklands war when the discovered that a missile hit does not spell the doom of the ship but having the ship catch fire due to the aluminum structure igniting does. Modern ships are also slower than WW2 ships stupidly enough, but I suspect that is more because you compare a modern DD to a WW2 DD and you should more reasonably compare it to a WW2 CA or CL.

Hmm, conflicting information. When I tried to find data on not only the ships above, but also further other destroyers and frigates, I could never find any information about any armor, despite for the WW2 battleships, and of course the Nimitz. I thought that was due to that they indeed do not care about armor anymore. You don't happen to know any source for ship data that goes beyond wikis and the ~top 20 google results where I drew from?

I'm thinking that it's probably due to automation leading to denser more efficient use of space, as well as a conscious design effort to reduce cross section which improves top speed and fuel efficiency.
I love the effort that went to the chart and the diagram is excellent for getting such a simple concept across for a casual like myself.
Edit: wait, I had that backwards, modern ships are less dense so I'll completely ignore how wrong I was and instead suggest modern ships are built significantly more cheaply, lighter grade metal across the board, more plastics and composites etc. Even ignoring the actual hull most individual components that goes into a ship would be significantly lighter now than it was back in the 40's.

Just keep in mind that a naval ship must float.  This means it must have a final density that is less than water.  A spacecraft does not need to float, but (obviously not in aurora) needs to consider that the acceleration it can achieve (which determines its velocity) is limited by being the Force applied divided by the mass of the ship...where mass is volume*density.

Thanks to trans-dimensional Cthulhu magic, Aurora ships don't accelerate though. However, needing not to care about mass at all when it comes to "acceleration" makes the other point about space ships being able to afford to be more dense even more prominent. This would indeed mean that (Aurora) space ships could be smaller than the naval drawn average V/M ratio would suggest, but I think first that it only appears to some degree, as modern ships are still already mostly made out of metals, so the amount you can add to that shouldn't be too groundbreaking unless you start to intentionally include lead for randomness' sake. Then secondly I would argue that the direct comparison of Aurora and Naval ships stands very strongly, as it seems to come up with the same data on given ships masses, namely for example the crew count, which after further lookups turned out to be pretty much parallel. Since a more dense ship should be smaller, this would normally result in Aurora ships then having lesser crews on same sizes, but they actually even got a bit more. This strongly suggests similar built.
It doesn't dispel the point completely though, and I agree that it may be wise to consider the V/M ratio as a mere upper limit, where normally all ships should be a bit smaller, and a bit denser than that.

As a first guess Aurora ships size is determined primarily by the volume needed for the crew space.  Work stations, maintenance spaces, walk ways, mess halls, kitchens, medical facilities, sleeping areas and toilets probably define the volume of most of the ship.  Missile magazines, cargo, fuel, hangers spaces probably are the other major volume components.  These are also the "low density" components of the ship being largely air.  After that you have the various plants and things like beam weapons which are mass intensive but volumetrically small.

I don't quite know what you mean with "Aurora ship sizes suggest volume needed for crew space". The only thing that determines crew are exactly the components that require them, so a mere tanker for example has very little of that, as tanks run without technicians, and complex war ships with military grade engines need a relatively high ratio.
Then also the volume needed for the crew space is definitely not primary part on Aurora ships, though I also agree it should be in reality and for flavor's sake. Crew quarters in Aurora presumably already include all that medical, supply storage, oxygen refinement, etc.etc. space, but still on my current destroyers (20k ships with 6 month deployment time) this only accounts for about 4.3%, and 9.6% if you count in engineering spaces. A long range 300k cruiser (3 years deployment) comes to 19.7% in combination, but that is still not the most prominent part.

Also a cargo ship might be just a spar with a small-ish crew volume and mostly just empty space one attached containers to.

I am pretty sure it is legal to assume the cargo ships as being as big as if those cargo bays were full, because at some point they are, and this space will be needed. If anything, I would argue in the opposite direction, that cargo ships might even be bigger, because cargo space here is not given in volume, like it should be on a space ship, so you could fill that available space with super heavy neutronium that would weight way more than a standard cargo container assumes to make place for.
Counter argument could be that mass still matters for jump ships and detection though, so that may be why there is a "loading limit" in any case. Kind of shady, but can be accepted under suspension of disbelieve I guess.

To determine an average size of an aurora ship you first need to know the approximate density of any particular component and that defines the volume it occupies if you accept the mass as a given.  Or you need to know its approximate volume (if you figure that is correct) and then knowing the density you find the ships final mass. 

Again, since the naval comparison fits so tight with Aurora as it does, I think it is reasonable to at least consider this average ratio to be a good guide. A grand average through all components is just good enough then, so even if it was possible, I think calculation per component wouldn't really improve much on that.

[sloanjh]

Hmm, conflicting information. When I tried to find data on not only the ships above, but also further other destroyers and frigates, I could never find any information about any armor, despite for the WW2 battleships, and of course the Nimitz. I thought that was due to that they indeed do not care about armor anymore.

I think there are two things here getting a little comingled.  My understanding/recollection is (no references):

1)  What is the structural metal above the waterline?  WWII was steel.  Post-WWII, aluminum was used to reduce top-weight (improving stability/allowing more weapons and sensors higher up).  Belknap collision pointed out this is a bad idea with respect to fires, at which point USN started going back to steel.  On the other hand, I was talking to a shipyard guy a couple of weeks ago at a conference, and he told me that they've gone back to aluminum for the new LCS designs.

2)  Armor.  In WWII, entire external hull was heavily armored.  Post-WWII, that changed to internal armor (some of it Kevlar) on critical compartments, e.g. magazines and/or engines. 

John

[Vandermeer (OP)]

2)  Armor.  In WWII, entire external hull was heavily armored.  Post-WWII, that changed to internal armor (some of it Kevlar) on critical compartments, e.g. magazines and/or engines.

With the internal armor, do you mean just the practice of building in a bulkhead compartment scheme? I read that became modern relatively late in western war ships, despite chinese ships employing this with wood since ancient times. In that case this shouldn't change too much, because it is more about floodgates and structural integrity other than actually stopping blasts.
If not, and there ware serious walls of armor internally, then how much are we speaking about? Is it comparable to the former outside armor just being scrapped and re-erected inside?

---
Anyway, for now I have completed the adjustment that basically still assumes that the outer shell of modern ships has no armor thicker than any other structural steel wall in the ship. This table came out:



It was done by figuring out what Aurora ships would have as armor on the given mass, which is luckily easily doable thanks to the uniform calculation rule from before. Then I just reduced the Volume by the percentage that this armor would take away from the original ship's mass, and added the Volume that this mass would fill as steel armor (assuming 8 tons/m³ here), which is of course something less than what was subtracted due to the higher density, so the final volume comes out smaller. It fulfills this formula:



There was also some mistake on the previous sum up that I detected in the excel file, so the former V/M rate was actually 4.49 instead of 4.57, and the crew suffered the same error.
Including also the new correction factor now, it comes out to this:


However, the average says not much in this case, as it is obvious that the impact of this correction weights a lot stronger on smaller ships again, while the big carriers only suffer a small raise in density. Also, this chart is of course only based on basic 1-layer designs, and will shift dramatically as even more armor is added. Without a mathematical rule, there will be no clear prediction, as the corrected V/M depends on layer count and technology.
I feel like the rule behind this should be relatively easy though, but I cannot put the finger on it yet. One very interesting thing I found out though from the chart of the former post, is that Aurora (conventional) armor weights exactly 6.25t per "area", whatever that area unit is. If it was square-meter (it isn't..), then the armor would be amazing 78 centimeters thick with just one layer! (again assuming 8 tons/m³ steel density) But I am pretty sure a ship of 7kt and approximately 25km³ would have more outside area than just 130m². Just calculated: even a sphere has 4135m² for this volume, and a sphere is the best mass conserving form in existence.

So how to figure out what this area unit means? I have the feeling that this will be essential for an answer. With the sphere there is at least a lower limit, giving that "1 area" in Aurora is at minimum 32,33m², which gives a top maximum armor thickness of 2,4cm per layer. Less than 2 in cube shape, and ever down with rising complexity.
...That is not much, honestly. That makes me question if the exclusion of armor weight was really justified. I think even standard hulls should have 1cm steel at least, right?
...Maybe this problem solves itself, and I have not to come up with a correction at all, as the naval ships are actually accurate? If I use the original ~27920m³ of the Sachsen frigate, it comes to 4450.7m² as sphere, and thus minimum 34.77m² per area, resulting in maximum thickness of 2.25cm, and 1.8 as cube.
V/M=4.5 confirmed or not?